into the model, it is most likely that the radio-
metric calibration data provided by Moniteq are
too high for all of the bands. Another normaliza
tion approach should, therefore, be used to
convert the raw data directly into reflectances
without using the calibration data. For this
purpose, different parameters have to be included
in the correction procedure; namely, the
reflectance of the water body in the scene plus
the extinction coefficients derived from the
atmospheric model. Other options available in the
ISDA software are relative normalization
techniques such as flat field normalization, equal
energy normalization, and the apparent reflectance
approach (Roberts et al., 1986; Jet Propulsion
Laboratory, 1985; Iqbal, 1983). For our
classification purposes for this paper, however,
it was not necessary to normalize the data.
Additional problems were encountered applying the
radiometric calibration values to the data set.
A substantial increase of the noise level in the
spectral domain could be detected, especially
within the first 100 bands (430 - 560 nm). A
reduction of the noise can be achieved due to the
utilization of a cubic spline algorithm or the
averaging of the signal in adjacent bands. The
second method results in a noise reduction of /2,
but it allows the possibility that some informa
tion in the spectral domain is lost, depending
upon the band characteristics (sampling interval,
bandwidth) and the data analysis to be performed.
Averaging of two adjacent bands is not that
critical for the PMI data because of the narrow
sampling interval (1.3 nm) and the overlapping of
the bands (1.3 nm).
Aircraft Attitude Variations
Geometric distortions of the PMI data caused by
aircraft motion (pitch, roll, and yaw) could not
be compensated for due to the lack of navigation
data (an inertial platform was not available) and
the nature of the data acquisition process. As
mentioned earlier, the PMI sensor works in a rake
mode providing forty profiles and not a contiguous
image. Thus, for example, it is not possible to
shift an image line for a specific number of
pixels in order to account for the distortion
caused by the roll parameter. For the purposes of
this study, a geometrically rectified data set was
not necessary in order to combine the ground
information with the PMI data because of the
obvious location of the agricultural objects in
the image.
CLASSIFICATION
Classification of high-resolution spectral data
is a challenging task due to the large number of
bands (up to 288) involved. Analysis methods are
required that take advantage of the high spectral
resolution to extract the most information while
minimizing the computation time. Two possible
classification methodologies are: (1) full
spectrum classification; and (2) feature
selection, followed by classification. An example
of the first method (Piech and Piech, 1989; Mazer
et al., 1987) combines techniques for a symbolic
representation of the spectrum derived for each
pixel with similarity measures used for
classification purposes. The second method uses
techniques and transformations for data reduction
and extraction of the most useful information
(Rundquist and Di, 1989). This approach permits
one to use image classification software already
implemented in existing image analysis systems.
A data reduction procedure, band-moment
(Rundquist and Di, 1989), was applied to
band PMI data set in order to reduce the
dimensionality. The formulae for the
case are:
Band moments:
1 N
M„ = — E [i*> * f(i)]
i=l
analysis
the 268-
spectral
discrete
(1)
Mean:
M,
M„
Central band moments:
1 N
P* = E [(i-i) p *f(i)]
i=l
Skewness :
Yi =
P
3/2
Kurtosis:
Y* =
P*
Concentrated-band moment :
1 N
P~ = -5- E [ (i- I i-i I T*f(i)]
i=l
(2)
(3)
(4)
(5)
(6)
where p = 0,1,2, ... is the moment order; N is the
number of bands; i = 1, ... N, is the band number;
and f(i) is the pixel intensity in DN for band i.
Since the bands are evenly spaced, one can use
either band number or the wavelength for this
calculation. This technique was applied in the
spectral domain on each pixel resulting in eight
central band moments as follows: (1) mean, (2)
ordinary moment (Mo), (3) variance (p 2 ), (4) 3rd
moment, (5) 4th moment, (6) skewness, (7)
kurtosis, and (8) band-concentrated moment(p 2ci ).
The computed real values of these eight moments
were then transformed linearly into an 8-bit data
set. In five of the eight bands, the images seem
to be similar. However, an improvement in the
information content, especially for the agricul
tural objects, could be detected when compared
with original single-band or three-band data
sets. The images for the moments 4, 6, and 7 are
different and appear visually to have less infor
mation content.
A feature selection procedure, the branch and
bound algorithm as described by Goodenough et al.
(1978), was used to determine the globally best
subset of bands involving the following classes
(sizes in pixels): wheat (230), barley (155),
corn (232), potatoes (94), fallow (151), mixed
grass (239), water (212), and forest (234). The
results for these training data are shown in Table
3. The best four-band subset was (1,6,7,8),
corresponding, respectively, to the following
moments: mean, skewness, kurtosis, and the band
concentrated moment. The average pairwise trans
formed divergence of the selected classes was used
to select the best subset. For each subset, a
maximum likelihood classification was carried out,
resulting in the weighted mean classification
accuracy and standard error of the mean (s.e.m.)
given in Table 3. The classification accuracies
were weighted by the frequencies of occurrence of
each class.
554
